72.2.8 problem 8

Internal problem ID [14643]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 06:45:59 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=2 y-t \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 15

dsolve([diff(y(t),t)=2*y(t)-t,y(0) = 1/2],y(t), singsol=all)
 

\[ y = \frac {t}{2}+\frac {1}{4}+\frac {{\mathrm e}^{2 t}}{4} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 35

DSolve[{D[y[t],t]==2*y[t]-t,{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{2 t} \left (2 \int _0^t-e^{-2 K[1]} K[1]dK[1]+1\right ) \]